Question

4. The final grades in a Biostatistics course (1) were compared with the final grades in a general elementary statistics course (2). Simultaneous boxplots of the two data sets are given below 1 I- 2 + - +- +-. -+-- -+-- 16 32 48 64 80 96 a) Which course tends to have higher grades? b) Which course tends to have more variable grades? c) Using the notes for Dotplots provided on page 17 to determine the 'step' size. Then, for cach course find approximate values for (1) the sample median and the first and third quartiles (2) the maximum and minimum grades (3) the interquartile range d) From the computer output below, select the numerical measures which support your answers to (a) and (b) above. Make any required additional calculations to achieve your answer St Dev Minimum 17.69 Variable Mean Q1 Median Q3 Maximum 80.75 99.00 C1 80 65.07 14.00 53.00 63.00 C2 76 72.09 13.80 42.00 61.50 74.00 84.75 94.00

Answer 1

(a) Course 2 has higher median and tends to have higher grades

(b) Course 1 with wider Inter Quartile Range tends to have more variable grades

(c)

(1) already answered in table provided in part d

(2) already answered in table provided in part d

(3) C1 IQR = 80.75 - 53 = 27.75

C2 IQR = 84.75 - 61.5 =23.25

(d) C2 has both higher mean and median, hence ans (a) is justified; C1 has higher standard deviation, hence ans (b) is also justified